Sam can paint the house in 7 days by himself, while Betty can paint the same house in 42 days. How long would it take Sam and Betty to paint the same house together?

It would take 6 days for Sam and Betty to paint the same house together.

Step-by-step explanation:

Let x represent the time it takes ( in days ) to complete painting the house working together. Our approach here is to add the rates of the two people, equal to the total rate, or 1 / 7.

Sam's rate = 1 / 7 ( 7 days to paint 1 house ),

Betty's rate = 1 / 42 ( 42 days to paint 1 house )

1 / 7 + 1 / 42 = 1 / x - now let us solve for x, our solution

1 / 7 + 1 / 42 = 1 / x ( multiply either side by 42x )

7x = 42,

x = 42 / 7 = 6 days

so, converting firstly the mixed fractions to improper fractions and then "adding".

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